Question: Simplify; express your answer in exponential form. Assume $n\neq 0, y\neq 0$. $\dfrac{{n^{5}y^{5}}}{{(n^{5}y^{3})^{-2}}}$
Answer: To start, try simplifying the numerator and the denominator independently. In the numerator, we can use the distributive property of exponents. ${n^{5}y^{5} = n^{5}y^{5}}$ On the left, we have ${n^{5}}$ to the exponent ${1}$ . Now ${5 \times 1 = 5}$ , so ${n^{5} = n^{5}}$ Apply the ideas above to simplify the equation. $\dfrac{{n^{5}y^{5}}}{{(n^{5}y^{3})^{-2}}} = \dfrac{{n^{5}y^{5}}}{{n^{-10}y^{-6}}}$ Break up the equation by variable and simplify. $\dfrac{{n^{5}y^{5}}}{{n^{-10}y^{-6}}} = \dfrac{{n^{5}}}{{n^{-10}}} \cdot \dfrac{{y^{5}}}{{y^{-6}}} = n^{{5} - {(-10)}} \cdot y^{{5} - {(-6)}} = n^{15}y^{11}$